Liquid Film Coating a Fiber as a Model System for the Formation of Bound States in Active Dispersive-Dissipative Nonlinear Media

Duprat, Camille; Giorgiutti-Dauphiné, F.; Tseluiko, Dmitri; Saprykin, Sergey; Kalliadasis, Serafim

doi:10.1103/physrevlett.103.234501

Cited by 53 publications

(42 citation statements)

References 15 publications

(8 reference statements)

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“…In particular, the absolute phase velocity of the analyzed solitary waves is a function of the ratio of inertia and viscous effects, see Eq. (33). Surface tension and gravity, on the other hand, have no discernible influence on the dispersion of solitary waves, contrary to the dispersion relation described by linear wave theory.…”

Section: Dispersion Of Solitary Wavesmentioning

confidence: 48%

“…These solitary waves have a dominant elevation with a long tail and steep front, typically with capillary ripples preceding the main wave hump. The γ 1 and γ 2 waves are also observed in falling films in the presence of various complexities, such as Marangoni effects due to heating, localized or uniform [22][23][24][25][26], chemical reactions [27][28][29], surfactants [30] and substrate curvature [31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

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Self-similarity of solitary waves on inertia-dominated falling liquid films

et al. 2016

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We propose the first consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization of solitary waves. Direct numerical simulations of the entire two-phase system are conducted using a state-of-the-art finite volume framework for interfacial flows in an open domain that was previously validated against experimental film-flow data with excellent agreement. We present a detailed analysis of the wave shape and the dispersion of solitary waves on 34 different water films with Reynolds numbers Re = 20 − 120 and surface tension coefficients σ = 0.0512 − 0.072 N m −1 on substrates with inclination angles β = 19 • − 90 • . Following a detailed analysis of these cases we formulate a consistent characterization of the shape and dispersion of solitary waves, based on a newly proposed scaling derived from the Nusselt flat film solution, that unveils a self-similarity as well as the driving mechanism of solitary waves on gravity-driven liquid films. Our results demonstrate that the shape of solitary waves, i.e. height and asymmetry of the wave, is predominantly influenced by the balance of inertia and surface tension. Furthermore, we find that the dispersion of solitary waves on the inertia-dominated falling liquid films considered in this study is governed by non-linear effects and only driven by inertia, with surface tension and gravity having a negligible influence.

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Section: Dispersion Of Solitary Wavesmentioning

confidence: 48%

Section: Introductionmentioning

confidence: 99%

Self-similarity of solitary waves on inertia-dominated falling liquid films

et al. 2016

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“…We would also like to point out that the leading-order system obtained here, (4.10), has a crucial difference from the systems obtained for the description of pulse interactions in local equations (see, e.g., [16,51,55]). For local equations which have pulses with exponentially decaying tails, it is sufficient to take into account only the immediate neighbors for each pulse, whereas for nonlocal equations we have to include long-range interactions due to the algebraically decaying tails of the pulses.…”

Section: Weak-interaction Theory For Solitary Pulsesmentioning

confidence: 99%

“…The decay of the tails is then found to be exponential (unless there are zero roots of the characteristic equation), and the rates and the nature (monotonic or oscillatory) of the decay are determined by the roots of the characteristic equation; see, e.g., [29] for the analysis for the gKS equation. We remark here that for local equations that have pulses with exponentially decaying tails, coherent structure theories have been developed in [5,9,16,39,40,41,42,51,55,56].…”

Section: Asymptotic Behavior Of the Tails Of A Single-pulse Solutionmentioning

confidence: 99%

“…For example, sufficiently large δ in the gKS equation regularizes the chaotic behavior of the KS equation, and solutions evolve into arrays of weakly interacting pulses of approximately the same shape, resembling the one-hump infinite-domain pulse (see, e.g., [2,9,16,28,51,55,56]). Note that the regularizing effect of dispersion has also been observed in other "local" equations, e.g., the related Nikolaevskiy equation [46].…”

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confidence: 99%

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Coherent Structures in Nonlocal Dispersive Active-Dissipative Systems

Lin¹,

Pradas

Kalliadasis

et al. 2015

SIAM J. Appl. Math.

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Abstract. We analyze coherent structures in nonlocal dispersive active-dissipative nonlinear systems, using as a prototype the Kuramoto-Sivashinsky (KS) equation with an additional nonlocal term that contains stabilizing/destabilizing and dispersive parts. As for the local generalized Kuramoto-Sivashinsky (gKS) equation (see, e.g., [T. Kawahara and S. Toh, Phys. Fluids, 31 (1988), pp. 2103-2111]), we show that sufficiently strong dispersion regularizes the chaotic dynamics of the KS equation, and the solutions evolve into arrays of interacting pulses that can form bound states. We analyze the asymptotic characteristics of such pulses and show that their tails tend to zero algebraically but not exponentially, as for the local gKS equation. Since the Shilnikov-type approach is not applicable for analyzing bound states in nonlocal equations, we develop a weak-interaction theory and show that the standard first-neighbor approximation is no longer applicable. It is then essential to take into account long-range interactions due to the algebraic decay of the tails of the pulses. In addition, we find that the number of possible bound states for fixed parameter values is always finite, and we determine when there is long-range attractive or repulsive force between the pulses. Finally, we explain the regularizing effect of dispersion by showing that, as dispersion is increased, the pulses generally undergo a transition from absolute to convective instability. We also find that for some nonlocal operators, increasing the strength of the stabilizing/destabilizing term can have a regularizing/deregularizing effect on the dynamics.

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Thin film flow of the water‐based carbon nanotubes hybrid nanofluid under the magnetic effects

et al. 2020

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In this article, the effects of magnetic field versus the thin liquid film water‐based ferrum oxide (Fe3O4) and carbon nanotubes (CNTs) nanofluids have been studied through stretching cylinder. The iron oxide and CNTs (single‐wall [SWCNTs] or multi‐wall [MWCNTs]) have been used as nanoparticles in carrier fluid water (H2O). To the flow field, magnetic effects are applied vertically. The modeled system of partial differential equations are transformed to nonlinear ordinary differential equations by selecting variables. The analytic solution has been obtained through homotopy analysis method. The obtained results are further compared with the numerical ND‐solve method. The embedded constraints impacts are focused on pressure distribution, velocity profile, heat transfer, Nusselt number, and Skin friction through graphical illustration and tables. The dispersion of Fe3O4 and CNTs in base fluid significantly enhanced the mechanism of heat transfer. Moreover, from the results, it has been observed that the MWCNTs have a greater impact on heat transfer, velocity, and pressure profile.

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Liquid Film Coating a Fiber as a Model System for the Formation of Bound States in Active Dispersive-Dissipative Nonlinear Media

Cited by 53 publications

References 15 publications

Self-similarity of solitary waves on inertia-dominated falling liquid films

Self-similarity of solitary waves on inertia-dominated falling liquid films

Coherent Structures in Nonlocal Dispersive Active-Dissipative Systems

Thin film flow of the water‐based carbon nanotubes hybrid nanofluid under the magnetic effects

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